The work, for example, of determining the measurements of damaged vehicle chassis and of straightening (aligning) such chassis is normally carried out with the chassis secured to an alignment bench with the aid of chassis clamps attached, for instance, to the pinch weld connecting the doorsill assembly and the vehicle floor to the chassis. The pinch weld of vans and like light trucks or lorries is not strong enough for this purpose, and consequently it is necessary to support the chassis of such vehicles at other attachment locations, with the aid of separate clamps of particular construction. Hitherto, however, no such clamp has been proposed which is totally reliable in operation and which can be secured to the chassis with sufficient precision and with sufficient clamping effect.